{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 卡方分布（Chi-Squared Distribution）\n",
    "***\n",
    "## 定义\n",
    "\n",
    "通俗的说就是通过小数量的样本容量去预估总体容量的分布情况\n",
    "\n",
    "卡方检验就是统计样本的实际观测值与理论推断值之间的偏离程度\n",
    "\n",
    "若n个相互独立的随机变量ξ₁，ξ₂，...,ξn ，均服从标准正态分布（也称独立同分布于标准正态分布），则这n个服从标准正态分布的随机变量的平方和构成一新的随机变量，其分布规律称为卡方分布（chi-square distribution）\n",
    "\n",
    "自由度：假设你现在手头有 3 个样本，。因为样本具有随机性，所以它们取值不定。但是假设出于某种原因，我们需要让样本均值固定，比如说，  ， 那么这时真正取值自由，”有随机性“ 的样本只有 2 个。 试想，如果  ,那么每选取一组  的取值，  将不得不等于  对于第三个样本来说，这种 “不得不” 就可以理解为被剥夺了一个自由度。所以就这个例子而言，3 个样本最终\"自由\"的只有其中的 2 个。不失一般性，  个样本， 留出一个自由度给固定的均值，剩下的自由度即为  。\n",
    "\n",
    "卡方检验的基本思想是根据样本数据推断总体的频次与期望频次是否有显著性差异\n",
    "\n",
    "## 公式\n",
    "\n",
    "$$\n",
    " \\begin{equation}\n",
    "    f(x|k) =\n",
    "    \\begin{cases}\n",
    "      \\frac{x^{\\frac{k}{2}-1}e^{-\\frac{x}{2}}}{2^{\\frac{k}{2}}\\Gamma(\\frac{k}{2})}, & \\text{if}\\ x>0 \\\\\n",
    "      0, & \\text{otherwise}\n",
    "    \\end{cases}\n",
    "  \\end{equation}\n",
    "$$<br>\n",
    "where\n",
    "$$ \\Gamma(n) = (n-1)! $$<br>\n",
    "and $k$ denotes the degrees of freedom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(-2,1.1,'Depicted below are the normed probability density function (pdf) and the cumulative density\\nfunction (cdf) of a Chi-Squared distributed random variable $ y \\\\sim \\\\chi^{2}(k) $, given $k$=4.')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Oe2NUV1cjNjZW+G97e3up1tPW1kaPHj1EXvbfvn2LY8eOsa4THx8vUitq/PjxGDlypNhy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\nh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YVlDz9ayZFjZB8+Wm4XPnIMAACAto3QEAAAtB3RqtRNTN57XYGP3pIRi+73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\n0FbFogo/+UvlPDBdZkXDP3+c7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YbHjQEAAAAA2iJCQwBo7RxbkUfvkPXlyozDyWFHKnrZ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\nAAAAADIfoSGATsn9wRtyrfgsbs286lbZfctS3BEAA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MgEhIZAF+X8fJ5cX8Y5/MThkHnN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\nGhIREREREREREVGA/we91IryXO/bWgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa5fd2f7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPORTS\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.style as style\n",
    "from IPython.core.display import HTML\n",
    "\n",
    "# PLOTTING CONFIG\n",
    "%matplotlib inline\n",
    "style.use('fivethirtyeight')\n",
    "plt.rcParams[\"figure.figsize\"] = (14, 7)\n",
    "\n",
    "plt.figure(dpi=100)\n",
    "\n",
    "# PDF\n",
    "plt.plot(np.linspace(0, 20, 100), \n",
    "         stats.chi2.pdf(np.linspace(0, 20, 100), df=4) ,\n",
    "        )\n",
    "plt.fill_between(np.linspace(0, 20, 100),\n",
    "                 stats.chi2.pdf(np.linspace(0, 20, 100), df=4) ,\n",
    "                 alpha=.15,\n",
    "                )\n",
    "\n",
    "# CDF\n",
    "plt.plot(np.linspace(0, 20, 100), \n",
    "         stats.chi2.cdf(np.linspace(0, 20, 100), df=4),\n",
    "        )\n",
    "\n",
    "# LEGEND\n",
    "plt.xticks(np.arange(0, 21, 2))\n",
    "plt.text(x=11, y=.25, s=\"pdf (normed)\", alpha=.75, weight=\"bold\", color=\"#008fd5\")\n",
    "plt.text(x=11, y=.85, s=\"cdf\", alpha=.75, weight=\"bold\", color=\"#fc4f30\")\n",
    "\n",
    "# TICKS\n",
    "plt.xticks(np.arange(0, 21, 2))\n",
    "plt.tick_params(axis = 'both', which = 'major', labelsize = 18)\n",
    "plt.axhline(y = 0, color = 'black', linewidth = 1.3, alpha = .7)\n",
    "\n",
    "# TITLE, SUBTITLE & FOOTER\n",
    "plt.text(x = -2, y = 1.25, s = r\"Chi-Squared $(\\chi^{2})$ Distribution - Overview\",\n",
    "               fontsize = 26, weight = 'bold', alpha = .75)\n",
    "plt.text(x = -2, y = 1.1, \n",
    "         s = 'Depicted below are the normed probability density function (pdf) and the cumulative density\\nfunction (cdf) of a Chi-Squared distributed random variable $ y \\sim \\chi^{2}(k) $, given $k$=4.',\n",
    "         fontsize = 19, alpha = .85)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## 自由度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(-1.5,2.5,'Depicted below are three Chi-Squared distributed random variables with varying $ k $. As one can\\nsee the parameter $k$ smoothens the distribution and softens the skewness.')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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icO3aNRgZGckt69atG7p16wYAuHTpEmeg6t1331UrzbKUvQ751qFDB3z11Vdyk3VMnz4d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\n0un5LbbYIr7zne90+gtRZWVlXHjhhTFlypRoamqKq6++Oq6++uqCYz7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DkB5FIrIFMpudlh2URAvl/4lwwjGfeEOR2d+ZWOxtX8qkeHuR8B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\nREREREQODA2JiIiIiIiIiIjI4f8BhbLQaLBmW0QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa5f22cf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=100)\n",
    "\n",
    "# PDF k = 1\n",
    "plt.plot(np.linspace(0, 15, 500), \n",
    "         stats.chi2.pdf(np.linspace(0, 15, 500), df=1),\n",
    "        )\n",
    "plt.fill_between(np.linspace(0, 15, 500),\n",
    "                 stats.chi2.pdf(np.linspace(0, 15, 500), df=1),\n",
    "                 alpha=.15,\n",
    "                )\n",
    "\n",
    "# PDF k = 3\n",
    "plt.plot(np.linspace(0, 15, 100), \n",
    "         stats.chi2.pdf(np.linspace(0, 15, 100), df=3),\n",
    "        )\n",
    "plt.fill_between(np.linspace(0, 15, 100),\n",
    "                 stats.chi2.pdf(np.linspace(0, 15, 100), df=3),\n",
    "                 alpha=.15,\n",
    "                )\n",
    "\n",
    "# PDF k = 6\n",
    "plt.plot(np.linspace(0, 15, 100), \n",
    "         stats.chi2.pdf(np.linspace(0, 15, 100), df=20),\n",
    "        )\n",
    "plt.fill_between(np.linspace(0, 15, 100),\n",
    "                 stats.chi2.pdf(np.linspace(0, 15, 100), df=6),\n",
    "                 alpha=.15,\n",
    "                )\n",
    "\n",
    "# LEGEND\n",
    "plt.text(x=.5, y=.7, s=\"$ k = 1$\", rotation=-65, alpha=.75, weight=\"bold\", color=\"#008fd5\")\n",
    "plt.text(x=1.5, y=.35, s=\"$ k = 3$\", alpha=.75, weight=\"bold\", color=\"#fc4f30\")\n",
    "plt.text(x=5, y=.2, s=\"$ k = 6$\", alpha=.75, weight=\"bold\", color=\"#e5ae38\")\n",
    "\n",
    "\n",
    "# TICKS\n",
    "plt.tick_params(axis = 'both', which = 'major', labelsize = 18)\n",
    "plt.axhline(y = 0, color = 'black', linewidth = 1.3, alpha = .7)\n",
    "\n",
    "# TITLE, SUBTITLE & FOOTER\n",
    "plt.text(x = -1.5, y = 2.8, s = \"Chi-Squared Distribution - $ k $\",\n",
    "               fontsize = 26, weight = 'bold', alpha = .75)\n",
    "plt.text(x = -1.5, y = 2.5, \n",
    "         s = 'Depicted below are three Chi-Squared distributed random variables with varying $ k $. As one can\\nsee the parameter $k$ smoothens the distribution and softens the skewness.',\n",
    "         fontsize = 19, alpha = .85)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.78735877974\n",
      "\n",
      "[ 2.98892946  2.76456717  2.76460459  9.29942882  5.73341246  2.262156\n",
      "  4.93962895  3.99792053  0.43182989  1.34248457]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chi2\n",
    "\n",
    "# draw a single sample\n",
    "np.random.seed(42)\n",
    "print(chi2.rvs(df=4), end=\"\\n\\n\")\n",
    "\n",
    "# draw 10 samples\n",
    "print(chi2.rvs(df=4, size=10), end=\"\\n\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Density Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KebKU8sVSylIp5WO3ef2hUso/2Hj9t0spRza99pMbx79YSvnh+xf9wRi1i2YB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\nAAAANPb/A4phFIRAm9+2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa5f969a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import chi2\n",
    "\n",
    "# additional imports for plotting purpose\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"figure.figsize\"] = (14,7)\n",
    "\n",
    "\n",
    "\n",
    "# continuous pdf for the plot\n",
    "x_s = np.arange(15)\n",
    "y_s = chi2.pdf(x=x_s, df=4)\n",
    "plt.scatter(x_s, y_s, s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cumulative Probability Density Function¶"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(X <=3) = 0.4421745996289252\n",
      "P(2 < X <= 8) = 0.6441806878992138\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import chi2\n",
    "\n",
    "# probability of x less or equal 0.3\n",
    "print(\"P(X <=3) = {}\".format(chi2.cdf(x=3, df=4)))\n",
    "\n",
    "# probability of x in [-0.2, +0.2]\n",
    "print(\"P(2 < X <= 8) = {}\".format(chi2.cdf(x=8, df=4) - chi2.cdf(x=2, df=4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
